T-star interconnection network topology

ABSTRACT

According to one embodiment of the present invention, a system for network communication includes an M dimensional grid of node groups, each node group including N nodes, wherein M is greater than or equal to one and N is greater than one and each node comprises a router and intra-group links directly connecting each node in each node group to every other node in the node group. In addition, the system includes inter-group links directly connecting each node in each node group to a node in each neighboring node group in the M dimensional grid.

BACKGROUND

The present invention relates to data networks, and more specifically,to an improved topology for nodes in a data network.

An exemplary data network transmits data, such as data in the form ofpackets, between nodes or users on the network. Each node may performoperations independently or may cooperate to transmit data between nodesin the network. In some cases the nodes include routers and/or switches,where links connect the nodes to one another. The links may bebi-directional, thus allowing data transmission in either directionbetween the nodes.

Larger data networks may lead to increased latency for communicationbetween nodes that have a long path between a source and destinationnode. This can be caused by a large number of links the data musttraverse to reach the destination node. Further, complex data networkshaving a large number of nodes and links may also experience faults morefrequently. Faults in the network can lead to re-routing of datatransmission between nodes, thus, also contributing to increased latencyfor data transmissions.

SUMMARY

According to one embodiment of the present invention, a system fornetwork communication includes an M dimensional grid of node groups,each node group including N nodes, wherein M is greater than or equal toone and N is greater than one and each node comprises a router andintra-group links directly connecting each node in each node group toevery other node in the node group. In addition, the system includesinter-group links directly connecting each node in each node group to anode in each neighboring node group in the M dimensional grid.

According to one embodiment of the present invention, a system fornetwork communication includes a grid including an M dimensional grid ofnode groups comprising nodes, each node group including N nodes,intra-group links directly connecting each node in each node group toevery other node in the node group, and inter-group links directlyconnecting each node in each node group to a node in each neighboringnode group in the M dimensional grid, the nodes each including a router.In addition, the system is configured to perform a method includingtransmitting a packet from a first node in a first location in a firstnode group to a second node in a corresponding first location in asecond node group and transmitting the packet from the second node inthe corresponding first location in the second node group to a thirdnode in a second location in the second node group.

Additional features and advantages are realized through the techniquesof the present invention. Other embodiments and aspects of the inventionare described in detail herein and are considered a part of the claimedinvention. For a better understanding of the invention with theadvantages and the features, refer to the description and to thedrawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The subject matter which is regarded as the invention is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The forgoing and other features, and advantages ofthe invention are apparent from the following detailed description takenin conjunction with the accompanying drawings in which:

FIG. 1 is a diagram of a portion of an exemplary system for a datanetwork;

FIG. 2 is a detailed view of an embodiment of a node group, such as nodegroups that are depicted in FIG. 1;

FIG. 3 is a diagram of an embodiment of a mesh network or grid; and

FIG. 4 is a diagram of an embodiment of a torus network or grid.

DETAILED DESCRIPTION

Embodiments of a system and method for a network topology, which may bereferred to as a T-Star topology, in some embodiments include a grid ofnode groups organized in a mesh or torus. Each node group includes aplurality of nodes, each node including a router, where an all-to-allnode group configuration provides direct connection between each node ineach node group by intra-group links. Further, links between nodes indifferent node groups, called inter-group links, are provided betweennodes in neighboring node groups, where the inter-group links areparallel direct connections from each node in each node group to a nodein a neighboring node group. The position of the node within eachneighboring node group receiving the inter-group link may be the same,thus providing parallel connection from each node to each of theneighboring node groups. The network data system and topology providereduced latency compared to a standard torus network with the samenumber nodes for network communication, reduced-length transmissionpaths as well as deadlock-free routing.

In an embodiment, the node groups are connected via a globalmultidimensional torus where g denotes the number of nodes in a groupand the nodes within the group are labeled i=0, . . . , g−1. Further, Mmay refer to the dimensionality of the torus, where each node group hasa global torus address indicating the coordinate of the group in an Mdimensional torus. The dimensions are referred to as 0, 1, . . . M−1 anda node group is identified by its coordinates (x₀, x₁, . . . x_(M-1)).Alternatively the dimensions and coordinates may be given symbolicnames. For an example used below, if M=6, the dimensions may be referredto as A, B, C, D, E and F and coordinates may be referred to as (a, b,c, d, e, f). Then, in the global torus network embodiment, node i in agroup has 2M connections to a node i in the neighboring groups. Forexample, in a network system utilizing embodiments of the topology withg=6 and M=2, each node in a node group has a direct link to the other(g−1) nodes in the group. Thus, in the example there are 5 suchintra-group links from each node and there are 4 inter-group links fromeach node.

The nodes may each include a router. In some embodiments, the nodes mayinclude a router, a main processor, a memory device and a processingelement located in the memory device. The nodes are organized into nodegroups, where the node groups are organized in a grid, which may be amesh or torus topology.

In an embodiment where the grid is a torus in every dimension, it wrapsso that every node group has 2M neighboring groups. For example, ifthere are N(A) nodes in dimension A labeled a=0, . . . , N(A)−1, thenthe node group with coordinate (a, b, c, d, e, f) is connected toneighboring node groups as follows. In the described relationship, %denotes a modular operation. In the example, node i in group (a, b, c,d, e, f) is connected to node i in neighboring group ((a+1) % N(A), b,c, d, e, f) and to node i in neighboring group ((a+N(A)−1) % N(A), b, c,d, e, f). In the embodiment, there are similar connections to nodes innode groups in the other dimensions. Examples of neighboring node groupsare also discussed below with reference to FIGS. 1-4.

In a mesh embodiment for the network grid, node groups on the edge ofthe mesh in a dimension have only 1 connection for that dimension. Forexample, (0, b, c, d, e, f) is connected only to (1, b, c, d, e, f) inthe A dimension and (N(A)−1, b, c, d, e, f) is connected only to(N(A)−2, b, c, d, e, f) in the A dimension (N(A)>1). In particular, nodei in group (0, b, c, d, e, f) is connected to node i in neighboringgroup (1, b, c, d, e, f) for the A dimension and node i in neighboringgroup (N(A)−1, b, c, d, e, f) is connected only to node i in group(N(A)−2, b, c, d, e, f) in the A dimension.

With reference now to FIG. 1, a diagram of a portion of an exemplarysystem for a data network 100 is shown. The data network 100 is arrangedin a grid, where the grid may be a torus or a mesh topology. The datanetwork 100 includes a node group 102, node group 104, node group 106,node group 108, node group 110, node group 112, node group 114, nodegroup 116 and node group 118. The node group 102 includes a node 120 ina first position, node 122 in a second position, node 124 in a thirdposition and node 126 in a fourth position. Similarly, node group 104includes a node 130 in a first position, node 132 in a second position,node 134 in a third position and node 136 in a fourth position. Othernode groups are arranged in similar fashion, where node group 106includes nodes 140, 142, 144 and 146; node group 108 includes nodes 150,152, 154 and 156; node group 110 includes nodes 160, 162, 164 and 166;node group 112 includes nodes 170, 172, 174 and 176; node group 114includes nodes 180, 182, 184 and 186; node group 116 includes nodes 190,192, 194 and 196; and node group 118 includes nodes 200, 202, 204 and206. The grid may be any suitable dimension (M dimensional grid) for anapplication, such as 1, 2, 3, 4, 5, 6, 7 or 8 dimensions in anembodiment. Other embodiments may have 9 or more dimensions. The numberof nodes in a node group is greater than one and can vary from two toany number of nodes. Embodiments may include 2, 3, 4, 5, 6, 7, 8, 9, 10or more (N nodes) for a particular application. As depicted, the grid isa two dimensional grid with four nodes per node group. A pure Mdimensional torus can be thought of as having a group size of 1 (g=1).

In an embodiment, each of the nodes in each node group are directlyconnected to each other in an all-to-all fashion. For example,intra-group links 210 in node group 102 directly connect each node toeach other node in the group. Further, inter-group links directlyconnect each node in each node group to a node in each neighboring nodegroup. For example, node 120 is connected directly to nodes 130 and 150in neighboring node groups 104 and 108, by inter-group links 212 and214, respectively. In an embodiment where the data network 100 system isa mesh, node group 102 is a corner group that has neighboring nodegroups 104 and 108. Further, node group 104 has neighboring node groups102, 106 and 110. In addition, node group 110 has neighboring nodegroups 104, 108, 112 and 116. The direct connections provided by theinter-group links are parallel connections, as a node is connected to asingle node in each neighboring node group. For instance, inter-grouplinks are provided to connect node 120 to node 150, node 122 to node152, node 124 to node 154 and node 126 to node 156. In an embodiment,the network provides connections from a node to nodes in the sameposition within neighboring node groups. For example, node 162 isconnected via inter-group links to nodes 152, 132, 172 and 192, wherenodes 152, 132, 172 and 192 are all in the second position within theirrespective groups. Further, the source or originating node (node 162from the prior example) may also be in the same position (secondposition). As depicted, the nodes in node group 110 will have directconnections to a selected number of nodes in neighboring node groups,where the selected number equals 2M which is twice the number ofdimensions (M) for the grid.

Embodiments may support deterministic routing or a form of dynamicrouting in which the next hop between a source node and a destinationnode is chosen from a set of most efficient or profitable hops,depending on network conditions. In a torus network, virtual channels(VCs) are used to prevent deadlock, e.g., there may be one or moredynamic VCs per direction/link and an appropriate “bubble escape” VC toprevent deadlocks. VCs are known to one of ordinary skill in the art. Inan embodiment, each VC represents a buffer inside the network forstoring packets. Without proper use of VCs, deadlocks can occur whenthere is a cycle of full VCs thus preventing packets from moving sincethere is no available buffer space to store another packet anywhere inthe cycle of full VCs. In addition, a “bubble escape” VC is also knownto those of ordinary skill in the art. In an embodiment; for eachdimension on the torus there is a bubble escape VC and packets require 2tokens to enter the VC but only 1 token to continue along the same VC,where a token represents buffer space for a full-sized packet. Such VCsmay exist for each type of packet traffic. For example, a packet traffictype may be a user-level request, user-level response, user-levelacknowledgment, a system-level request, system-level response, orsystem-level acknowledgment. Accordingly, VCs may be provided and usedby each inter-group and intra-group link in a network to prevent networkdeadlocks.

In an embodiment of the system using dynamic routing, a minimal path, ina network without faults, requires at most one intra-group link, alsoreferred to as “L” hop, and multiple inter-group links, also referred toas “D” hops, to reach its destination. Hops refer to transmission pathsbetween nodes (inter-group and intra-group) for data, such as packets,to enable network communication. For deterministic routing, the L hopmay be taken first, on the source node group including the source node,or last, on the destination node group including the destination node.For dynamic routing, we may permit multiple L hops, in any group, toavoid contention on the D inter-group links. So at any node, a packetmay make a D hop in an efficient or profitable direction, or an L hop,depending on traffic conditions within the network. To prevent infinitecycles of hops within a group, a limit may be placed on the number of Lhops that a packet can make in each group. The number of L hops may bestored in the packet (initially 0) and incremented whenever an L hop istaken. When reaching a programmable limit, L hops are no longerpermitted in that group, except on the destination node group in whichonly the L hop to the final destination node is permitted. When thepacket moves to the next group, the L hop counter in the packet is resetto 0. Alternatively, there may be a total limit on the total number ofdynamic L hops a packet can make as it traverses the network. To preventdeadlocks, for each type of traffic, there may be 0, 1 or more dynamicVCs per D link and one bubble escape VC per D link. There may also be 0,1 or more dynamic VCs per L link and one escape VC per L link. When apacket is on a node, it has a unique escape VC such as the bubble escapeVC described earlier. If there are more D hops required, the escape VCmay be ordered according to some (programmable) dimension order, such asa network with M=6, the order may be A first, then B, then C, then D,then E, then F. For example, with this ordering, if all the A and B hopshave been taken but there are still C hops to be taken, then the escapeVC is the escape VC on the D link in the (profitable) C direction. Whenall D hops are completed, and the node is on the destination group, theescape VC is on the L link to the final destination. Alternatively, onecould order the links such that the L hop is taken first, followed bydimension-ordered D hops.

In an embodiment using indirect L-routing, a packet may be required totake more than 1 L hop. If indirect L routes are permitted, an extra VCon each L link would be needed, otherwise a cyclic dependency VCs can becreated which could result in deadlocks. The indirect route would thenhave the first hop to be an L hop, then all D hops (if any), followed bya final L hop. There may be a dynamic number of L hops permitted on theintermediate groups. This embodiment has at least 2 VCs per L link (foreach type of traffic), and 3 VCs per L link if dynamic hops arepermitted.

In an embodiment of the network, one well known approach to thoseskilled in the art to fault tolerance in a torus network is to set upintermediate destination nodes and route communication through theintermediate node so as to avoid any failed node or link. To avoiddeadlocks an extra VC is used for each type of traffic, one for routingfrom the source node to the intermediate node and then the packetswitches to a second VC when going from the intermediate node to thedestination node

In an embodiment of the network there are g parallel paths betweenadjacent groups and, if a node fails, that node can be avoided by notpermitting any L or D hops into the failed node (or link). In anexample, a certain D hop must be taken over a link to the next node.That next node is failed, or if the link to it is failed, that link andnode can be avoided by taking an L hop to a different node in the groupfollowed by a D hop to the next adjacent group.

Several approaches to fault tolerance in the presence of one or morenode failures may be implemented. In an embodiment, where links andnodes on the source node group from node id “s” to a node location id“m” are working. There are at least 2 L VCs labeled L1 and L2. The hopfrom s to m is taken using VC L1. Note that m may be equal to s, inwhich case no L hop is made. Torus plane m from the source group to thedestination group contains no faults. There is 1 D VC, labeled D1, andthis is used for routing to the destination group. On the destinationgroup, if m is not equal to the destination node id “d”, then VC L2 isused to route from m to the destination node d. Both nodes m and d andthe (bidirectional) links between them must be working.

In another embodiment, to permit more flexibility, switching planes onintermediate groups is permitted. Embodiments provide deadlock-freeoperation for a broad range of node failures. If a node in a node groupeither fails or must be taken down to replace a faulty node, then theintermediate node routing approach may be used to avoid the faultyboard. An intermediate board/group is specified and an extra escape VCfor the D links is used (for each traffic type).

In an embodiment with optical connections between node groups, such as aboard containing nodes/routers, a “spare” chip is added containingrouting logic to the board. Each node in the node group adds a link tothe spare. The spares are connected globally in an M dimensional torus.The spare can operate in pass-through mode, in which the bytes of thepacket are simply passed from an input to a programmable output. If a Dlink fails in some direction j on node i, packets for that direction aresent to the spare over the local link, then to the spare on the nextboard in direction j, then from the spare to node i.

In an application where one of the nodes in each group is a spare, thenupon a failure of node f on a board the spare node s becomes logicalnode f on that board. To prevent also moving the corresponding nodes fon adjacent boards, node f sends its data to the spare node on itsboard. The spare is operating in pass-through mode, as described above,and sends its data to logical node f (physical node s) on the board withthe failed nodes. Provided there are not failed nodes on adjacentboards, and no pass-through path is required than once, the applicationcan be re-configured and run, avoiding the failed node. This providesthe appearance of a fault-free partition in which case the otherfault-tolerant routing methods earlier need not be invoked.

FIG. 2 is a detailed view of an embodiment of a node group 250, such asnode groups that are depicted in FIGS. 1, 3 and 4. The node group 250includes node 252, node 254, node 256 and node 258. Each of the nodesare directly connected to each other node in the group via intra-grouplinks 260. In addition, each of the nodes in the group are connected inparallel to a node in each neighboring node group in the grid viainter-group links 262.

FIG. 3 is a diagram of an embodiment of a mesh network 300 or grid,where the mesh network 300 is a 2-dimensional network (“M-dimensionalgrid”) of node groups. The node groups in the mesh network 300 mayinclude any suitable number of nodes in any suitable configuration, suchas the node group 250 in FIG. 2. As depicted, the mesh network 300 is a2-dimensional 4×4 network of 16 node groups. Node groups 302, 304, 306and 308 form a first side edge of the mesh, while node groups 326, 328,330 and 332 form a second side edge of the mesh network 300. Further,node groups 302, 310, 318 and 326 form a top edge and node groups 308,316, 324 and 332 form the bottom edge of the mesh network 300. Nodegroups 312, 314, 320 and 322 are central node groups in the network. Inthe mesh network 300, nodes in the central node groups have inter-grouplinks to a node in each of four neighboring groups. For example, eachnode in node group 312 has inter-group links to a node in each of nodegroups 310, 304, 314 and 320. In the mesh network 300, nodes in edgegroups have two or three inter-group links to a node each neighboringgroup, depending on the node group location in the mesh. For example,node group 302 is a corner node group with two inter-group links foreach node to nodes in neighboring groups 304 and 310. In addition, nodegroup 310 is a side node group with three inter-group links for eachnode to nodes in neighboring groups 302, 318 and 312. Thus, depending onthe node group location, the number of links from a node to adjacentnode groups is less than or equal to 2 M (e.g., 2×2=4).

FIG. 4 is a diagram of an embodiment of a torus network 400 or grid,where the torus network 400 is a 2-dimensional network of node groups.The node groups in the torus network 400 may include any suitable numberof nodes in any suitable configuration, such as the node group 250 inFIG. 2. As depicted, the torus network 400 is a 2-dimensional 4×4network of 16 node groups. Node groups 402, 404, 406 and 408 form afirst side edge of the mesh, while node groups 426, 428, 430 and 432form a second side edge connected by links 450 to the first side edge ofthe torus network 400. Further, node groups 402, 410, 418 and 426 form atop edge and node groups 408, 416, 424 and 432 form the bottom edgeconnected by links 460 to the top edge of the torus network 400. Nodegroups 412, 414, 420 and 422 are central node groups in the network. Inthe torus network 400, each node in each of the node groups haveinter-group links to a node in each of four neighboring node groups. Forexample, each node in node group 412 has inter-group links to a node ineach of node groups 410, 404, 414 and 420. Further, node group 402 is acorner node group with four inter-group links for each node to nodes inneighboring groups 404, 408, 426 and 410. In addition, node group 410 isa side node group with four inter-group links for each node to nodes inneighboring groups 402, 418, 416 and 412.

Technical effects of embodiments of a system and method for a networktopology are provided that include a grid of node groups organized in amesh or torus. Each node group includes a plurality of nodes, each nodeincluding a router, where an all-to-all network node group configurationprovides direct connection between each node in each node group byintra-group links. Further, inter-group links are provided betweenneighboring node groups, where the inter-group links are parallel directconnections from each node in a node group to a node in a neighboringnode group. The network data system and topology provide reduced latencyfor communication compared to a regular torus, reduced-lengthtransmission paths as well as deadlock-free routing. The intra-grouplinks and inter-group links provide a network with a shortest pathbetween an source node in a first node group and a destination node in asecond node group, the shortest path including at most one intra-grouplink and at least one inter-group link

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of onemore other features, integers, steps, operations, element components,and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated

The flow diagrams depicted herein are just one example. There may bemany variations to this diagram or the steps (or operations) describedtherein without departing from the spirit of the invention. Forinstance, the steps may be performed in a differing order or steps maybe added, deleted or modified. All of these variations are considered apart of the claimed invention.

While the preferred embodiment to the invention had been described, itwill be understood that those skilled in the art, both now and in thefuture, may make various improvements and enhancements which fall withinthe scope of the claims which follow. These claims should be construedto maintain the proper protection for the invention first described.

What is claimed is:
 1. A system for network communication, the systemcomprising: an M dimensional grid of node groups, each node groupcomprising N nodes, wherein M is greater than or equal to one, N isgreater than one, and each node comprises a router; intra-group linksdirectly connecting each node in each node group to every other node inthe node group; inter-group links directly connecting, in parallel, eachnode in a position in each node group to a node in a corresponding sameposition in each neighboring node group in the M dimensional grid ofnode groups; a first node group of the M dimensional grid of node groupsincluding a source node; a neighboring node group of the M dimensionalgrid of node groups including a destination node; and a path between thesource and the destination nodes including a first direct parallelinter-group link of the inter-group links and a first intra-group linkof the intra-group links, wherein each node in the first node groupcomprising: a direct parallel inter-group link to a single node in eachof a selected number of neighboring node groups of the M dimensionalgrid of node groups, wherein the selected number of neighboring nodegroups is less than or equal to 2 M neighboring node groups, whereineach node group comprises a spare node that operates as a pass-throughin case of a fault in the M dimensional grid of node groups, wherein theneighboring node group is a second node group, wherein a firstinter-group link directly connects, in parallel, a first node in thefirst node group to a second node in the second node group, wherein thefirst node and second node are each in a first position with respect tothe first node group and second node group, wherein a second inter-grouplink directly connects, in parallel, a third node in the first nodegroup to a fourth node in the second node group, and wherein the thirdnode and fourth node are in a second position with respect to the firstand second node groups.
 2. The system of claim 1, wherein the pathcomprising at most one intra-group link and at least one inter-grouplink.
 3. The system of claim 1, wherein the path comprising intra-grouplink from the source node and at least one inter-group link to thedestination node.
 4. The system of claim 1, wherein the path comprisingat least one inter-group link from the source node and intra-group linkto the destination node.
 5. A system for network communication, thesystem comprising: an M dimensional grid of node groups comprisingnodes, each node group comprising N nodes; wherein M is equal to orgreater than one, N is greater than one; intra-group links directlyconnecting each node in each node group to every other node in the nodegroup; and inter-group links directly connecting, in parallel, each nodegroup to a selected number of nodes in each neighboring node group,wherein the selected number equals 2M and, the nodes each comprising arouter, the system configured to: transmit a packet along a path from asource node in a location in the first node group to a destination nodein a neighboring node group to the first node group, wherein the pathbetween the source and the destination nodes including a first directparallel inter-group link of the inter-group links and a firstintra-group link of the intra-group links and transmit the packet fromthe destination node to a third node in a second location in a secondnode group wherein each node in the first node group comprises: a directparallel inter-group link to a single node in each of a selected numberof neighboring node groups of the M-dimensional grid of node groups,wherein the selected number of neighboring node groups comprises lessthan or equal to 2M neighboring node groups, and wherein each node groupcomprises a spare node that operates as a pass-through node in case of afault in the M dimensional grid of node groups.
 6. The system of claim5, wherein the path comprising at most one intra-group link and at leastone inter-group link.
 7. The system of claim 5, wherein the pathcomprising an intra-group link from the source node and at least oneinter-group link to the destination node.
 8. The system of claim 5,wherein the path comprising at least one inter-group link from thesource node and an intra-group link to the destination node.
 9. A systemfor network communication, the system comprising: a grid comprising: anM dimensional grid of node groups comprising nodes, each node groupcomprising N nodes, intra-group links directly connecting each node ineach group to every other node in the node group, and inter-group linksdirectly connecting, in parallel, each node in a position in each nodegroup to a respective single node in a corresponding same position ineach neighboring node group, the nodes each comprising a router, thesystem configured: transmit a packet along a path from a source node ina location in a first node group to a destination node group to thefirst node group, wherein the path between the source and thedestination nodes including a first direct parallel inter-group link ofthe inter-group links and a first intra-group link of the intra-grouplinks, and transmit the packet from the destination node to a third nodein a second location in the second node group, wherein each node in thefirst node group comprises: a direct parallel inter-group link to asingle node in each of a selected number of neighboring node groups ofthe M dimensional grid of the node groups, wherein the selected numberof neighboring nodes comprises less than or equal to 2M neighboring nodegroups, and wherein each node group comprises a spare node that operatesas a pass-through in case of a fault in the M dimensional grid of nodegroups.
 10. The system of claim 9, wherein the path comprising at mostone intra-group link and at least one inter-group link.
 11. The systemof claim 9, wherein path comprising an intra-group link from the sourcenode and at least one inter-group link to the destination node.
 12. Thesystem of claim 9, wherein t path comprising at least one inter-grouplink from the source node and an intra-group link to the destinationnode.